Section on Statistical Education JSM 2010

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1 Understanding Students Attitudes toward Statistics: New Perspectives Using an Expectancy-Value Model of Motivation and the Survey of Attitudes Toward Statistics Caroline Ramirez 1, Esma Emmioglu 2, Candace Schau 3 1 University of California, Davis, CA 2 Middle East Technical University, Ankara, Turkey 3 CS Consultants, LLC, Albuquerque, NM Abstract Many statistics educators believe that students attitudes toward statistics are important. We assert that current educational achievement motivation models, especially Eccles Expectancy-Value Model (EVM), can assist us in understanding these attitudes. We have reframed the EVM, applying it to students enrolled in statistics courses. We show the congruence between EVM and the Survey of Attitudes toward Statistics or SATS. We then describe how this Model and the SATS can be important in statistics education, both in evaluating and improving instruction and in research. (Abstract ID: ) Key Words: Students' attitudes, SATS, statistics education, statistics achievement 1. Introduction For at least the last two decades, the National Council of Teachers of Mathematics has recognized the effects of students attitudes and motivation in math achievement and persistence on school tasks (NCTM, 1989, 1991). Further, motivation has emerged as the primary factor for understanding math achievement, ability beliefs and expectations for success (Wigfield & Eccles, 2000). Although motivation has been widely recognized for its importance in education, we believe that statistics educators can benefit from understanding students motivation and attitudes toward statistics. Considering that statistics coursework contributes to a statistically literate society, students overall motivation and attitudes deserve special attention. The objective of this paper is to help us realize that it is just as important to pay attention to students motivation and attitudes as to their learning of statistics because the motivation and positive attitudes that we foster in our students have lifelong implications. To assist us in understanding students attitudes and motivation, we use Eccles Expectancy-Value Model (EVM) as a theoretical framework and show its congruence to the Survey of Attitudes toward Statistics (SATS ). We explore the motivational constructs that Eccles and her colleagues (e.g., Eccles, O Neill, & Wigfield, 2005; Eccles & Wigfield, 2002; Wigfield & Eccles, 2000) have used in their research and juxtapose it with the constructs in the SATS, while emphasizing the multidimensional nature of attitudes and motivation. We then conclude with implications for statistics educators in the areas of pedagogy, research and evaluation. 830

2 2. Expectancy-Value Model of Motivation and Attitudes Eccles and her colleagues have developed a model that is designed to explain why some students perform differently from others in academic domains. Their Model (called Eccles EVM throughout the remainder of this paper) was based on earlier versions of Expectancy-Value Models; this class of models, especially Eccles EVM, has been a big influence on motivation research. They posit that students beliefs about how well they will do on a task (called Expectations for Success) and how much they value that task (called Subjective Task Value) are related. Eccles and colleagues theorize that students Expectations for Success and Subjective Task Value (STV) predict their achievement outcomes and that students are more likely to choose to engage in tasks (including enrolling in and completing courses) that they value and in which they expect to do well. In addition, Eccles EVM includes the factors of Stable Child Characteristics as well as Previous Achievement-Related Experiences, as well as other factors. Figure 1 shows a visual representation of their Model, and how these components and other variables interrelate. Figure 1: Eccles et al. expectancy-value model of achievement. Figure taken from Eccles & Wigfield, 2002, p.119. Reprinted with permission from the publisher. As Figure 1 shows, Subjective Task Value is further broken down into the following four factors: Attainment Value, Intrinsic Value, Utility Value and Cost. The importance a student attaches to the task is called Attainment Value. Intrinsic Value refers to the students interest in or enjoyment from engaging in the task. Utility Value links the usefulness of the task to the students future goals, such as their careers. Lastly, the Cost factor refers to why a student might try to avoid the task for example, fear of failure, task difficulty, or math anxiety. According to this model, Expectations for Success are positively influenced by high Attainment, Interest and Utility Values and negatively influenced by high Cost. Similarly, 831

3 Attainment, Interest, Utility and Cost Values are positively influenced by high Expectations for Success. A large body of research uses Eccles Expectancy-Value Model as a theoretical framework. This research supports the predictions made by Eccles EVM. Researchers have consistently found that students expectancy beliefs are related to the value that they place on a task. Research findings also indicate that STV and Expectations for Success predict students academic choices. For example, Wigfield and Eccles (2002) reported that these two components predicted course enrollment, even after controlling for prior academic performance. Based on a longitudinal study, Durik, Vida, and Eccles (2006) reported that the interest (intrinsic value) and importance that 4th graders gave to reading predicted the number of high school English courses these students chose to take. Similarly, Simpkins, Davis-Kean, and Eccles (2006) have shown that math and science activities in late elementary school predicted advanced math and science course selection in high school. Although much research has been conducted with students at the elementary and secondary school levels, we assert that Eccles EVM can assist us in understanding the motivation and attitudes of college students who take statistics courses. Furthermore, this Model is appropriate for exploring the relationship between students engagement with statistics and motivation. Eccles Expectancy-Value Model explores the links among achievement-related choices (e.g., enrolling in and completing statistics courses) and how students value statistics along with their expectations for success in statistics. In the next section, we have reframed Eccles EVM and applied it to examining the attitudes and motivation of students in statistics courses. We begin by introducing the Survey of Attitudes Toward Statistics (SATS ), a survey instrument congruent with Eccles EVM. 3. Application of Eccles EVM and the SATS The Survey of Attitudes Toward Statistics (SATS ) was developed by Schau and her colleagues (Schau, Stevens, Dauphinee, & DelVecchio, 1995) in the early 1990s. This instrument is usually administered twice, once at the beginning of a statistics course (Pretest) and once at the end (Posttest), although it can be administered more often. Thirty-six items on the SATS assess six components of attitudes; students respond to each item on a 7-point Likert response scale: 1 = Strongly Disagree ; 4 = Neither Disagree nor Agree (neutral); 7 = Strongly Agree. Higher item responses mean more positive attitudes, and responses to items that are negatively worded are reversed before scoring. Typically, students spend about minutes responding to the items on the SATS-36 administered in either a paper-and-pencil or a Web format. Additional references and the SATS instrument can be viewed at In the development of the SATS, Schau and her colleagues (e.g., Dauphinee, Schau, & Stevens, 1997; Schau, et al., 1995; Schau, 2003) used a seven-step process: (1) an initial examination of surveys purporting to assess students attitudes toward statistics; (2) written descriptions of introductory statistics students' attitudes; (3) qualitative data analysis by coding and sorting phrases into a consensus component structure by introductory statistics' students and instructors; 832

4 (4) pilot testing and subsequent revision of items written from these words and phrases; (5) validation of the internal component structure generated in Step 3 using Confirmatory Factor Analysis techniques; (6) validation of component scores based on their relationships and lack of relationships with scores from other measures, and (7) addition of two more attitude component scores. The SATS six Attitude Components include: Affect (6 items): Students feelings concerning statistics Example item - I am scared by statistics. Cognitive Competence (6 items): Students attitudes about their intellectual knowledge and skills when applied to statistics Example item - I can learn statistics. Value (9 items): Students attitudes about the usefulness, relevance, and worth of statistics in personal and professional life Example items - I use statistics in my everyday life. ; Statistics is not useful to the typical professional. Difficulty (7 items): Students attitudes about the difficulty of statistics as a subject Example item - Most people have to learn a new way of thinking to do statistics. Interest (4 items): Students level of interest in statistics Example item - I am interested in using statistics. Effort (4 items): Amount of work the student expends to learn statistics Example item - I plan to work hard in my statistics course. Along with these six components, the survey also includes items that assess Student Characteristics and Previous Achievement. Student Characteristics Examples include - Gender Date of Birth Major Previous Achievement Examples include - Current grade point average How good at mathematics are you? Consistent with Eccles EVM, the six attitude components of the SATS and the other included variables emphasize the multi-dimensional nature of attitudes and motivation. This kind of framework helps instructors and researchers consider the many factors that directly or indirectly affect students attitudes toward statistics and their statistics achievement-related choices, as well as how these relationships work. The SATS complements the work of Eccles and her colleagues by specifically combining and deconstructing some of the constructs that are relevant to college students in statistics courses. The first notable difference between the SATS and the EVM is in simplifying some of Eccles constructs by combining Self-Concept of One s Abilities and Expectation of Success into Cognitive Competence. Similarly, Previous Achievement-Related Experiences and Interpretations of Previous Experiences were 833

5 combined into Previous Achievement. Eccles included Attainment Value and Utility Value as separate STV factors, but these were combined in the SATS to form the Value component. Furthermore, Schau and colleagues deconstructed the Interest- Enjoyment STV factor in the EVM by forming the Interest and Affect components. This deconstruction occurred because, conceptually, students affective feelings toward statistics are not the same as their interest in statistics. In addition, measures of attitudes toward statistics historically have included Affect as a separate component (often in the form of statistics anxiety). We assert that students affect toward statistics is important in its own right. In the SATS, the EVM factors of Enjoyment and Affective Reactions are combined into the Affect component. We believe that Eccles EVM makes at least three important contributions in helping us understand students attitudes and motivation toward statistics. First, the multidimensional nature of the EVM theoretically validates the multi-component structure of the SATS. Two of the more frequently used measures of the attitudes of students in statistics courses included only one or two components. Roberts and Bilderback (1980) developed the Statistics Attitude Survey (SAS), which yields only a single attitude score. Similarly, Wise (1985) developed the Attitudes Toward Statistics Measure (ATS), which has two attitudinal components: Field and Course. Field describes the students attitudes toward the use of statistics in their field of study (p. 402), while Course taps into students attitudes toward their statistics course. The component structures of the SAS and the ATS fail to capture the complexity of the attitudes and motivation architecture, as indicated in Eccles EVM. Unlike these two, the SATS has six attitude components and so at least begins to capture this complexity. Second, the SATS and the EVM can be used effectively to describe the changes in attitudes and motivation over the course of learning, as evidenced by the longitudinal studies that Eccles and her colleagues have done. Although the SAS and the ATS can be used as a pre and post measure of students attitudes, there are problems with the content of some of the items in these instruments. For example, the SAS includes some survey items that assess students knowledge about statistics concepts or problems, not just their attitudes, which is problematic in administering the SAS at the beginning of an introductory course (Curda, 1997; Gal & Ginsburg, 1994; Rhoads & Hubele, 2000). Even though the definitions of the two ATS components are quite broad, some items do not appear to fit into their designated component or even into the other component (Gal & Ginsburg, 1994; Rhoads & Hubele, 2000). On the other hand, the SATS only assesses students attitudes and was designed to be administered as a Pre-test and Post-test to track changes in students attitudes. Finally, the complex architecture of the EVM allows for a more detailed look on how the attitude and other motivation factors interrelate. With attitudes functioning as the core in explaining the performance and choices of students, Eccles EVM allows us to extend their model into the domain of statistics, similar to the application of the EVM in the math domain or in any of the other academic domains. Although the EVM was originally developed to explain gender differences in math performance and course-taking patterns of high school and college students, the model has been applied to various academic and achievement domains, educational contexts, and cross-cultural studies. Therefore the 834

6 EVM has been acknowledged as an appropriate starting point or theoretical framework for investigating students attitudes and motivation toward a particular task or academic domain. We believe that the EVM has much potential to influence how statistics educators understand the phenomenon of motivation and learning. Table 1 shows the congruence among the theoretical constructs of Eccles EVM and the constructs measured by the SATS. This congruence supports the validity of the SATS constructs. The six attitude components, as well as Student Characteristics and Previous Achievement, of the SATS include all four of the Subject Task Value (STV) factors of the EVM, as well as other factors in the Model. Table 1: Congruence between SATS and the EVM SATS Attitude Components Affect Cognitive Competence Value Difficulty Interest Effort Additional Constructs: Student Characteristics Previous Achievement EVM Constructs Affective Reactions & Enjoyment Value Self-concept of One s Abilities & Expectation of Success Attainment Value & Utility Value Perception of: Task Demands Intrinsic Value Cost Stable Child Characteristics Previous Achievement-Related Experiences & Interpretations of Experience It is our contention that these important contributions of Eccles EVM to statistics education and their implementation in the SATS suggest new ways of analyzing and conceptualizing the attitudes and motivation of college students in statistics courses. Furthermore, we believe that the EVM-influenced elaborations found in the SATS also point to implications in the areas of pedagogy, research and evaluation. 4. Implications and Future Research It is important to note that this paper presents a theoretical review of Eccles' Expectancy- Value Model in relation to the Survey of Attitudes Toward Statistics. It is not intended to be a comprehensive review of the empirical literature on the EVM nor is it an empirical study using the SATS. We have shown that the constructs contained in the SATS align with many of the factors in Eccles EVM and that together they provide explanatory power regarding college students attitudes and motivation in statistics courses. With this in mind, we have a number of implications for teachers and researchers who are trying to improve students attitudes and motivation and their overall experience in statistics courses, as well as the quality of statistics instruction. First, in the area of pedagogy, a major course objective should include encouraging students to develop (or maintain) positive attitudes, because attitudes are just as important as their learning, especially in the introductory course. We recommend that statistics instructors evaluate changes in students attitudes across their courses. There is much evidence to support Eccles EVM that students expectations of success and their values 835

7 can predict achievement-related choices and performance both in and out of classes, but more research is needed, especially in the domain of statistics education. Second, we specifically suggest that, when selecting an instrument to use in measuring students attitudes and in evaluating statistics courses, researchers and instructors should consider using the SATS due to its good psychometric properties (e.g., Hilton, Schau, & Olsen, 2002; Tempelaar, Schim van der Loeff, & Gijselaers, 2007) and its congruence with the EVM. Similarly, researchers who are evaluating the impact of reform activities can benefit from using the SATS in examining changes in students attitudes, as well as in analyzing the potential impacts of course activities and instructional approaches on students attitudes. While statistics educators have always kept students learning front and center, students attitudes greatly impact their persistence in completing their statistics courses, their achievement outcomes, and their choices to enroll in additional statistics courses, along with their use of statistics in life. There is a clear need for more research studies using the SATS and for understanding statistics students attitudes in general. Finally, we encourage researchers to bridge the gap between statistics education reform (e.g., GAISE) and research on motivational / attitudinal dimensions of learning and instruction. Although motivational research has been increasing in the area of mathematics education, it lags behind in statistics education. It is our hope that this review helps others better understand the EVM and the SATS and encourages researchers and instructors to consider attitudes and motivation in their work. Acknowledgements The research reported in this paper was supported partially by the Consortium for the Advancement of Undergraduate Statistics Education (CAUSE), through NSF Award # We are grateful to for the organizers of the USCOTS 2009 (United States Conference On Teaching Statistics) for starting our Attitudes Research Cluster. References Curda, S. K. (1997). Learners' Motivational Characteristics in Statistics: A Causal Model. Norman: University of Oklahoma. Dauphinee, T. L., Schau, C., & Stevens, J. J. (1997). Survey of attitudes toward statistics: Factor structure and factorial invariance for women and men. Structural Equation Modeling: A Multidisciplinary Journal, 4(2), Durik, A.M., Vida, M., & Eccles, J. S. (2006). Task values and ability beliefs as predictors of high school literacy choices: A developmental analysis. Journal of Educational Psychology, 98, Eccles, J. S., O Neill, S. A., & Wigfield, A. (2005). Ability Self-Perceptions and Subjective Task Values in Adolescents and Children. Paper presented at the Child Trends Conference, Washington DC. Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. Annual Review of Psychology, 53, Gal, I., & Ginsburg, L. (1994). The Role of Beliefs and Attitudes in Learning Statistics: Towards an Assessment Framework. Journal of Statistics Education, 2(2). [Online: 836

8 Hilton, S.C., Schau, C., & Olsen, J.A. (2004). Survey of attitudes toward statistics: Factor structure invariance by gender and by administration time. Structural Equatıon Modeling, 11(1), National Council of Teachers of Mathematics (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, VA. National Council of Teachers of Mathematics (1991). Professional Standards for Teaching Mathematics. Reston, VA. Rhoads, T. R., & Hubele, N. F. (2000). Student attitudes toward statistics before and after a computer-integrated introductory statistics course. IEEE Transactions on Education, 43(2), Roberts, D.M. & Bilderback, E.W. (1980). Reliability and validity of a statistics attitude survey. Educational and Psychological Measurement, 40, Schau, C. (2003). Students' Attitudes: The "Other" Important Outcome in Statistics Education. Paper presented at the Joint Statistical Meeting - Section on Statistics Education, San Francisco, CA. Schau, C., Stevens, J., Dauphinee, T. L., & DelVecchio, A. (1995). The development and validation of the Survey of Attitudes toward Statistics. Educational and Psychological Measurement, 55(5), Simpkins, S. D., Davis-Kean, P. E., & Eccles, J. S. (2006). Math and science motivation: A longitudinal examination of the links between choices and beliefs. Developmental Psychology, 42(1), Tempelaar, D. T., Schim van der Loeff, S., & Gijselaers, W. H. (2007). A structural equation model analyzing the relationship of students' attitudes toward statistics, prior reasoning abilities and course performance. Statistics Education Research Journal, 6(2), Wigfield A. & Eccles J.S. (2000). Expectancy-value theory of achievement motivation. Contemporary Educational Psychology, 25(1), Wigfield A. & Eccles J.S. (2002). The development of competence beliefs and values from childhood through adolescence. In A. Wigfield and J.S. Eccles (Eds.), Development of Achievement Motivation (pp ). San Diego, CA: Academic Press. Wise, S. L. (1985). The development and validation of a scale measuring attitudes toward statistics. Educational and Psychological Measurement, 45,